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<p>Traditional three-dimensional (3D) multi-missile cooperative guidance often suffers from incomplete characterization of engagement dynamics, occasional large impact-time errors, and limited robustness, which undermines simultaneous arrival performance in complex 3D scenarios. To address these issues, this paper proposes a singular perturbation-based 3D cooperative guidance framework that decomposes the closed-loop system into a fast kinematic subsystem and a slow timing-coordination subsystem. The fast subsystem adopts augmented proportional navigation (APN) and ensures input-to-state stability (ISS) of the guidance loop. The slow subsystem models the communication network as an undirected connected graph and uses the Laplacian matrix to compute each missile’s time-to-go (TGO) deviation from the swarm mean, and a discrete-time consensus protocol then generates longitudinal velocity adjustment commands to drive the timing errors toward convergence. To suppress systematic bias and large outliers in TGO estimation, a residual architecture predictive neural network (PredictorNN) is introduced to predict and compensate cooperative error trends, and a multi-objective reward with dynamic weight scheduling forms a closed-loop “prediction–adjustment–verification” refinement mechanism. Monte Carlo simulations (1000 runs) benchmarked against APN show that the proposed method achieves a mean impact-time difference of 0.023&#xa0;s and a hit rate of 99.3%. Under extreme initial-position conditions, the mean time difference decreases from 2.28&#xa0;s (APN) to 0.2202&#xa0;s. Overall, the results demonstrate improved robustness while maintaining high interception accuracy, offering a practical solution for 3D multi-missile cooperative interception in challenging missions.</p>

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Three-Dimensional Time Cooperative Guidance Algorithm Based on an Improved Neural Network Predictor

  • 期刊论文

  • 发表日期：

    2026年7月26日

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  • Changyao Gao,
  • Shujin Bo,
  • Yun Chen,
  • Guoguang Wen

摘要

Traditional three-dimensional (3D) multi-missile cooperative guidance often suffers from incomplete characterization of engagement dynamics, occasional large impact-time errors, and limited robustness, which undermines simultaneous arrival performance in complex 3D scenarios. To address these issues, this paper proposes a singular perturbation-based 3D cooperative guidance framework that decomposes the closed-loop system into a fast kinematic subsystem and a slow timing-coordination subsystem. The fast subsystem adopts augmented proportional navigation (APN) and ensures input-to-state stability (ISS) of the guidance loop. The slow subsystem models the communication network as an undirected connected graph and uses the Laplacian matrix to compute each missile’s time-to-go (TGO) deviation from the swarm mean, and a discrete-time consensus protocol then generates longitudinal velocity adjustment commands to drive the timing errors toward convergence. To suppress systematic bias and large outliers in TGO estimation, a residual architecture predictive neural network (PredictorNN) is introduced to predict and compensate cooperative error trends, and a multi-objective reward with dynamic weight scheduling forms a closed-loop “prediction–adjustment–verification” refinement mechanism. Monte Carlo simulations (1000 runs) benchmarked against APN show that the proposed method achieves a mean impact-time difference of 0.023 s and a hit rate of 99.3%. Under extreme initial-position conditions, the mean time difference decreases from 2.28 s (APN) to 0.2202 s. Overall, the results demonstrate improved robustness while maintaining high interception accuracy, offering a practical solution for 3D multi-missile cooperative interception in challenging missions.